Infinite-sheet branching of the habitat of the natural frequencies of open resonators as a result of admission of infinite boundaries

摘要

Summary form only given. We consider several eigenvalue problems for the Helmholtz and Maxwell equations, where the fields are assumed time-harmonic, i.e. /spl sim/e/sup -ikct/, and the normalized frequency k is an eigenparameter: (1) localized 2D and 3D dielectric resonators (DR) in free space; (2) in PEC-wall waveguide; (3) in stratified dielectric medium; (4) a localized 3D DR in free space; (5), in a PEC-wall waveguide or stratified medium; and (6) and near a fiber. These problems are about the time-harmonic electromagnetic fields in and out of bounded penetrable objects placed in unbounded host medium. Their correct statement needs certain condition imposed on the field behavior at infinity. Such a condition, in each case, follows from the behavior of the corresponding Green's function analytically continued from the real values of k to the complex domain.